Wiskunde Multiple Choice Vraag

$\frac{\sqrt{10}-\sqrt5}{\sqrt{10}+\sqrt5}=$	A. 1
B.
C. 3
D. −1
E. $3-2\sqrt2$

$\frac{\sqrt{10}-\sqrt5}{\sqrt{10}+\sqrt5}=\frac{(\sqrt{10}-\sqrt5).(\sqrt{10}-\sqrt5)}{(\sqrt{10}+\sqrt5)(\sqrt{10}-\sqrt5)}=\frac{(\sqrt{10}-\sqrt5)^2}{10-5}=\frac{10+5-2\sqrt{50}}{5}=\frac{15-10\sqrt2}{5}=3-2\sqrt2$
$=\frac{10+5-2\sqrt{50}}{5}=\frac{15-10\sqrt2}{5}=3-2\sqrt2$